In your situation, a "pile of regular bleach" is exactly what you need to be shocking with--I bet if you have your ammonia tested, you'll find that it's high, which makes for a huge chlorine demand, as Watermom said. Unfortunately, the only way to overcome that is to keep adding chlorine (read: bleach) until you overcome the ammonia. The chlorine you're putting into the pool is getting used up quickly by "stuff" in your pool, as evidenced by the high CC reading--you have to get it to shock level (and maintain that level until the CC reading goes to 0) in order to get the pool clean.

Janet